Determine value $b$ in $f(x)=ab^x$ given the following data points

Question

If $f(x)=ab^x$, what is the value of $b$ if $(0,35)$ and $(3,125)$ are data points?

Is this the way to do it? $$35=ab^0,$$ $$a=35.$$ $$125=ab^3,$$ $$125=3\log(35)+\log(b),$$ $$41.667/\log(35)=\log(b),$$ $$41.667/1.544=\log(b).$$ If yes, now what?

Answer 1

By evaluation in 0 we obtain $a=ab^0=f(0)=35$

Now, valuating in 3, we have $b^3=f(3)/a=125/35= 25/7$ and $b$ is equal to the cubic root of $25/7$.